Determining the position of a photodetection event is useful in many circumstances, and various approaches have been developed for determining position. A conceptually straightforward approach is to employ a detector array having multiple small detector elements (i.e. pixels), each pixel being individually addressed, e.g., as considered in U.S. Pat. No. 6,080,984. However, a large number of electrical connections to the pixels can be required. For some applications, such as medical imaging by positron emission tomography (PET), the number of connections required by a pixelated detector array can be prohibitively large.
Accordingly, methods of determining the location of a photodetection event on the active surface of a single photodetector are also of interest. One approach is the so-called Anger algorithm, which has been known for a long time (e.g., it is described in U.S. Pat. No. 3,011,057), and is still in present-day use. The Anger algorithm is based on the idea of having multiple electrodes on the photodetector and computing event positions based on normalized differences of detector signals.
For example, FIG. 1 shows how the Anger algorithm would apply for the case of a square detector 102 having terminals TA, TB, TC, and TD at its corners. These terminals provide corresponding signals A, B, C, and D. The problem of interest is to determine the coordinates (XP, YP) of a photodetection event P from the signals A, B, C and D. According to the Anger algorithm, estimates for these coordinates are given by
                              X          P                =                                            (                              C                +                D                            )                        -                          (                              A                +                B                            )                                            A            +            B            +            C            +            D                                              (                  1          ⁢          a                )                                          Y          P                =                                            (                              A                +                D                            )                        -                          (                              B                +                C                            )                                            A            +            B            +            C            +            D                                              (                  1          ⁢          b                )            for the example of FIG. 1. The Anger algorithm is based on the assumption that terminal signals increase as the distance between P and the corresponding terminal decreases. For example, signal D from terminal TD would increase as the distance from P to TD decreases, and similarly for the other signals.
However, it is well known that location estimates provided by the Anger algorithm are not entirely accurate, with pincushion and/or barrel distortion being the most typical errors. This is not surprising, since the relation between event location and signal strengths provided by a photodetector in practice will not match the simple forms assumed in Eqs. 1a-b.
Accordingly, methods for compensating or correcting the position determination provided by the Anger algorithm have been investigated. Calibration maps or lookup tables have been employed in practice. Some such approaches have the significant drawback of being very time-consuming to implement (e.g., a single calibration run can take days). A trainable, model-based neural network position estimation algorithm is considered in US 2005/0151084.
However, a common feature of these compensation or correction methods is that they deal with correcting the results provided by an imperfect low-level position estimation algorithm (e.g., the Anger algorithm). Accordingly, it would be an advance in the art to provide improved position determination from a single, multi-electrode photodetector.